Sure, let's solve this step by step!
We are given the quadratic equation:
[tex]$(x + 2)^2 + 5(x + 2) - 6 = 0.$[/tex]
We want to find an equivalent form of this equation by making a substitution.
1. Substitution Step:
We will let [tex]\( u = x + 2 \)[/tex].
2. Rewrite the Equation:
Substitute [tex]\( u \)[/tex] in place of [tex]\( x + 2 \)[/tex] in the given equation:
[tex]$(u)^2 + 5(u) - 6 = 0.$[/tex]
3. Simplify:
Simplify the equation:
[tex]$u^2 + 5u - 6 = 0.$[/tex]
Hence, the quadratic equation equivalent to [tex]\((x + 2)^2 + 5(x + 2) - 6 = 0\)[/tex] after making the substitution [tex]\( u = x + 2 \)[/tex] is:
[tex]$u^2 + 5u - 6 = 0.$[/tex]
So, the correct answer to the given question is:
[tex]$u^2 + 5u - 6=0 \quad \text{where} \quad u=(x+2).$[/tex]
